In theory the American living abroad tax exemption can be applied to anyone who is legal US resident (GC or citizen). You need to pass a 330 day test. i.e. you must stay OUT of US for at least 330 days out of one calender year.
As a greed card holder, you also need to stay IN the US for 50% of a caldender year (resident period requirement for GC holder per INS regulations).
Unless you get a special exemption from INS regarding your GC resident requirement, you CAN'T satisfy BOTH the 330 day test for the tax exmption AND the GC 50% calender year resident requirement.
These are general rules, but there are ways to work around it on a case by case basis. Please consult a professional accountant AND/OR immigration attorney.
